3.2 Evolution over time by group
It is also interesting to see how this evolved over time within group.
HDI


Education Index


Life Expectancy Index


Income Index


HDI Male


HDI Female


I notice, as before, an overall positive trend, without Regions nor Development Categories overtaking each other. The one exception seems to be the HDI of Oceania which drops from 2nd place in 1990 to 4th place in 2015.
Europe ranks consistently at the top, and Africa at the bottom. See the comparsion of 1990 with 2015:
## Source: local data frame [5 x 8]
## Groups: year [1]
##
## year Region `Human Development Index` `Education Index`
## <int> <fctr> <dbl> <dbl>
## 1 1990 Africa 0.4227632 0.3046842
## 2 1990 Americas 0.6255556 0.5181852
## 3 1990 Asia 0.5880526 0.4560526
## 4 1990 Europe 0.7509714 0.6468571
## 5 1990 Oceania 0.6551667 0.6193333
## # ... with 4 more variables: `Life Expectancy Index` <dbl>, `Income
## # Index` <dbl>, `Human Development Index Male` <dbl>, `Human Development
## # Index Female` <dbl>
## Source: local data frame [5 x 8]
## Groups: year [1]
##
## year Region `Human Development Index` `Education Index`
## <int> <fctr> <dbl> <dbl>
## 1 2015 Africa 0.5299623 0.4612453
## 2 2015 Americas 0.7418000 0.6728286
## 3 2015 Asia 0.7209583 0.6405833
## 4 2015 Europe 0.8554146 0.8244390
## 5 2015 Oceania 0.6960909 0.6852727
## # ... with 4 more variables: `Life Expectancy Index` <dbl>, `Income
## # Index` <dbl>, `Human Development Index Male` <dbl>, `Human Development
## # Index Female` <dbl>
## Source: local data frame [2 x 8]
## Groups: year [1]
##
## year `Development Classification` `Human Development Index`
## <int> <fctr> <dbl>
## 1 1990 Developed 0.7622750
## 2 1990 Developing 0.5290865
## # ... with 5 more variables: `Education Index` <dbl>, `Life Expectancy
## # Index` <dbl>, `Income Index` <dbl>, `Human Development Index
## # Male` <dbl>, `Human Development Index Female` <dbl>
## Source: local data frame [2 x 8]
## Groups: year [1]
##
## year `Development Classification` `Human Development Index`
## <int> <fctr> <dbl>
## 1 2015 Developed 0.8623696
## 2 2015 Developing 0.6458944
## # ... with 5 more variables: `Education Index` <dbl>, `Life Expectancy
## # Index` <dbl>, `Income Index` <dbl>, `Human Development Index
## # Male` <dbl>, `Human Development Index Female` <dbl>
There is some apparent inconsistency: Oceania HDI is 0.69 in 2015, but HDI male and HDI female are both above 0.84. The HDI should be in between male and female . This is explained by the fact that some countries with low HDI have missing values for HDI male and female
3.3 Models
We put it all together in a panel model.
First in a random effects model in order to account for the regional grouping.
## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = HDR$`Human Development Index` ~ HDR$`Life Expectancy Index` +
## HDR$`Income Index` + HDR$Region, data = HDR, model = "random",
## index = c("Country", "year"))
##
## Unbalanced Panel: n=81, T=5-26, N=1770
##
## Effects:
## var std.dev share
## idiosyncratic 1.089e-03 3.300e-02 0.994
## individual 6.325e-06 2.515e-03 0.006
## theta :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01421 0.06078 0.06791 0.06186 0.06791 0.06791
##
## Residuals :
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.116753 -0.022287 0.004045 0.000018 0.023260 0.082693
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## (Intercept) -0.03735173 0.00551788 -6.7692 1.757e-11 ***
## HDR$`Life Expectancy Index` 0.46617730 0.01175431 39.6601 < 2.2e-16 ***
## HDR$`Income Index` 0.50476534 0.00786496 64.1790 < 2.2e-16 ***
## HDR$RegionAmericas 0.01434739 0.00317149 4.5239 6.477e-06 ***
## HDR$RegionAsia 0.00060373 0.00286004 0.2111 0.8328
## HDR$RegionEurope 0.03651343 0.00343599 10.6268 < 2.2e-16 ***
## HDR$RegionOceania 0.04389959 0.00425229 10.3237 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 47.077
## Residual Sum of Squares: 2.1636
## R-Squared: 0.95404
## Adj. R-Squared: 0.95027
## F-statistic: 6099.67 on 6 and 1763 DF, p-value: < 2.22e-16
Then in a fixed effect model
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = HDR$`Human Development Index` ~ HDR$`Life Expectancy Index` +
## HDR$`Income Index` + HDR$Region, data = HDR, model = "within",
## index = c("Country", "year"))
##
## Unbalanced Panel: n=81, T=5-26, N=1770
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.1003104 -0.0202519 0.0029314 0.0221676 0.0949724
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## HDR$`Life Expectancy Index` 0.4176441 0.0117657 35.4967 < 2.2e-16 ***
## HDR$`Income Index` 0.5130348 0.0075214 68.2097 < 2.2e-16 ***
## HDR$RegionAmericas 0.0231396 0.0031148 7.4288 1.734e-13 ***
## HDR$RegionAsia 0.0059363 0.0028436 2.0876 0.03698 *
## HDR$RegionEurope 0.0479038 0.0033645 14.2378 < 2.2e-16 ***
## HDR$RegionOceania 0.0519161 0.0041140 12.6194 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 44.057
## Residual Sum of Squares: 1.8325
## R-Squared: 0.95841
## Adj. R-Squared: 0.9113
## F-statistic: 6463.39 on 6 and 1683 DF, p-value: < 2.22e-16
And we select FE based on the Hausman test:
##
## Hausman Test
##
## data: HDR$`Human Development Index` ~ HDR$`Life Expectancy Index` + ...
## chisq = 584.13, df = 6, p-value < 2.2e-16
## alternative hypothesis: one model is inconsistent
The Fixed Effect model confirms the strong correlation between components.
However, since the HDI is an average of its components the result is not surprising, but more confirming. Therefore it is also interesting to run the models only based on the groupings :
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = HDR$`Human Development Index` ~ HDR$Region, data = HDR,
## model = "within", index = c("Country", "year"))
##
## Unbalanced Panel: n=187, T=10-26, N=4348
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.317610 -0.071566 -0.001540 0.062106 0.278657
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## HDR$RegionAmericas 0.2234687 0.0051786 43.152 < 2.2e-16 ***
## HDR$RegionAsia 0.1861820 0.0047754 38.988 < 2.2e-16 ***
## HDR$RegionEurope 0.3366026 0.0048258 69.751 < 2.2e-16 ***
## HDR$RegionOceania 0.2082969 0.0081909 25.430 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 114.78
## Residual Sum of Squares: 51.356
## R-Squared: 0.55259
## Adj. R-Squared: 0.52831
## F-statistic: 1283.54 on 4 and 4157 DF, p-value: < 2.22e-16
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = HDR$`Human Development Index` ~ HDR$`Development Classification`,
## data = HDR, model = "within", index = c("Country", "year"))
##
## Unbalanced Panel: n=187, T=10-26, N=4348
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.331641 -0.099554 0.019091 0.092464 0.306136
##
## Coefficients :
## Estimate Std. Error t-value
## HDR$`Development Classification`Developing -0.2277917 0.0046049 -49.467
## Pr(>|t|)
## HDR$`Development Classification`Developing < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 114.78
## Residual Sum of Squares: 72.272
## R-Squared: 0.37037
## Adj. R-Squared: 0.35435
## F-statistic: 2447.01 on 1 and 4160 DF, p-value: < 2.22e-16
Results confirm that developed countries have higher HDI, African countries are at the bottom and European at the top.
Finally, we saw the the Income Index was a good predictor of HDI:
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = HDR$`Human Development Index` ~ HDR$`Income Index`,
## data = HDR, model = "within", index = c("Country", "year"))
##
## Unbalanced Panel: n=81, T=5-26, N=1770
##
## Residuals :
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.2161860 -0.0311076 0.0089113 0.0372149 0.1382070
##
## Coefficients :
## Estimate Std. Error t-value Pr(>|t|)
## HDR$`Income Index` 0.8208594 0.0073159 112.2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 44.057
## Residual Sum of Squares: 5.2089
## R-Squared: 0.88177
## Adj. R-Squared: 0.84092
## F-statistic: 12589.3 on 1 and 1688 DF, p-value: < 2.22e-16
The results confirm that.